{
  "abstract": "Let $θ\\to \\mathcal G(θ)$ be a map from a parameter to the solution of some non-linear partial differential equation modelling a dynamical system. We provide conditions to show posterior consistency for $θ$ under observations of $\\mathcal G(θ)$ with dependent noise, modelling potential time-correlations of the sensors used to make the measurements. We provide two examples, namely the Navier-Stokes equations with unknown viscosity and initial condition, as well as a Reaction-Diffusion type equation with diffusivity coefficient that is varying (heterogeneous) in space, which requires novel stability estimates for a Darcy transport operator with accumulation in time.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07240",
  "author_total": 1,
  "authors": [
    {
      "name": "Aditya Jambhale"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2vwmd4r60a7g7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07240",
  "fulltext_url": null,
  "id": "2vwmd4r60a7g7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07240",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7220921290",
  "pdf_url": "https://arxiv.org/pdf/2610.07240",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2vwmd4r60a7g7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07240",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07240"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Posterior Consistency under dependent errors in non-linear inverse problems with applications to time evolution equations",
  "title_text": "Posterior Consistency under dependent errors in non-linear inverse problems with applications to time evolution equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:32Z",
  "url": "https://research.draconitic.com/paper/2vwmd4r60a7g7",
  "venue": "arXiv",
  "versions": []
}